New congruences for $2$-color partitions and $t$-core partitions

• Published in: Boletim da Sociedade Paranaense de Matemática Vol. 43
• Main Authors: Fathima, S. N., Pore, Utpal, Sriraj, M. A., Reddy, Polaepalli Siva Kota
• Format: Journal Article
• Language: English
• Published: 21.01.2025
• ISSN: 0037-8712; 2175-1188; 2175-1188
• DOI: 10.5269/bspm.70916

Let $c_N(n)$ denote the number of $2$-color partition of $n$ subject to the restriction that one of the colors appears only in parts that are divisible by $N$. If $t$ is a positive integer, then a partition of a nonnegative integer $n$ is a $t$-core if none of the hook numbers of the associated Ferrers-Young diagram is a multiple of $t$. Let $a_t(n)$ denote the number of $t$-core partitions of $n$. In this paper, we obtain new congruences modulo $3$ for the $2$-color partition function $c_{11}(n)$, $t$-core partition functions $a_5(n)$ and $a_{11}(n)$.